Problem: Evaluate the definite integral. $\int^{8}_{4}\big(-6x+5\big)\,dx = $
Solution: First, use the power rule: $\int^{8}_{4}\big(-6x+5\big)\,dx ~=~-3 x^2+5x\Bigg|^{{8}}_{4}$ Second, plug in the limits of integration: $\begin{aligned} &\phantom{=}\big[-3\cdot{8}^2+5\cdot{8}\big]-\big[-3\cdot{4}^2+5\cdot{4}\big] \\\\ &= -152 + 28 \\\\ &= -124 \end{aligned}$ The answer: $\int^{8}_{4}\big(-6x+5\big)\,dx ~=~ -124$